A tree-structured piecewise linear adaptive filter

The idea of a tree-structured piecewise linear adaptive filter is proposed. The tree-structured filter is constructed as follows. Each node in a binary tree is associated with a linear filter restricted to a polygonal domain, and this is done in such a way that each subtree is associated with a piecewise linear filter. A training sequence is used to adaptively update the filter coefficients and domains at each node, and to select the best subtree and the corresponding piecewise linear filter. The authors summarize the derivation and analysis of the tree-structured piecewise linear adaptive filter. They then investigate the performance of the tree-structured filter as an adaptive echo canceler and compare it with that of linear and truncated Volterra series adaptive echo cancelers through computer simulations